Details

analyze1.1s (16.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.2%	0.1%	7
32.8%	67.1%	0.1%	8
38.2%	61.7%	0.1%	9
41%	58.9%	0.1%	10
43.9%	56%	0.1%	11
45.4%	54.5%	0.1%	12
46.9%	53%	0.1%	13
47.6%	52.3%	0.1%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample3.4s (48.5%)

Results

1.2s	1114×	body	2048	valid
896.0ms	1310×	body	1024	valid
726.0ms	4415×	body	128	valid
399.0ms	912×	body	512	valid
163.0ms	501×	body	256	valid
13.0ms	4×	body	4096	valid

Compiler

Compiled 32 to 24 computations (25% saved)

preprocess14.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

4×	`associate-/r*_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	20	40
2	24	40
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`associate-/r*_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	12	20
2	14	20

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

32.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.1b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	6.2b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))
✓	25.8b	(tan.f64 (/.f64 x (*.f64 y 2)))
✓	26.0b	(sin.f64 (/.f64 x (*.f64 y 2)))

series60.0ms (0.9%)

Counts

3 → 72

Calls

18 calls:

8.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	x	0
6.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	y	0
6.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	x	-inf
6.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	x	inf
4.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	y	-inf

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`prod-diff_binary64`
522×	`log-prod_binary64`
180×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`
159×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	193	38
2	2642	38

Stop Event

1×	node limit

Counts

3 → 87

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

363×	`associate-/r/_binary64`
360×	`cancel-sign-sub-inv_binary64`
359×	`times-frac_binary64`
339×	`associate-/l/_binary64`
215×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	1410
1	187	1392
2	544	1326
3	2664	1299

Stop Event

1×	node limit

Counts

159 → 110

prune125.0ms (1.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	92	18	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	18	111

Error

23.2b

Counts

111 → 18

Alt Table

Status	Error	Program
	32.1b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)) (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))
	32.8b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 3))
	33.1b	(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	59.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	32.4b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))
	58.5b	(/.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (sin.f64 (/.f64 x (*.f64 y 2))))
▶	25.9b	(/.f64 1 (cos.f64 (*.f64 1/2 (/.f64 x y))))
	32.3b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	26.2b	1
	53.7b	(/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
	35.1b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 1/2 (/.f64 x y) (.f64 (pow.f64 (/.f64 x y) 3) -1/48)))
	32.1b	(pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) 3)
	54.1b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	32.9b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	32.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2) 1) (/.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (sin.f64 (.f64 (/.f64 x y) 1/2))))
	61.5b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 x y) 1/2)))) (sin.f64 1))))
	59.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	35.0b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))

Compiler

Compiled 3143 to 2127 computations (32.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/2 (/.f64 x y))
✓	0.1b	(/.f64 1 (cos.f64 (*.f64 1/2 (/.f64 x y))))
✓	25.9b	(cos.f64 (*.f64 1/2 (/.f64 x y)))

series29.0ms (0.4%)

Counts

3 → 24

Calls

18 calls:

5.0ms	(/.f64 1 (cos.f64 (*.f64 1/2 (/.f64 x y))))	y	0
3.0ms	(/.f64 1 (cos.f64 (*.f64 1/2 (/.f64 x y))))	x	inf
3.0ms	(/.f64 1 (cos.f64 (*.f64 1/2 (/.f64 x y))))	x	-inf
2.0ms	(/.f64 1 (cos.f64 (*.f64 1/2 (/.f64 x y))))	x	0
2.0ms	(/.f64 1 (cos.f64 (*.f64 1/2 (/.f64 x y))))	y	inf

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

827×	`log1p-expm1-u_binary64`
827×	`expm1-log1p-u_binary64`
243×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
84×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	185	28
2	2264	28

Stop Event

1×	node limit

Counts

3 → 68

simplify27.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

823×	`associate-/l*_binary64`
610×	`associate-/r*_binary64`
414×	`fma-def_binary64`
375×	`associate-*l/_binary64`
143×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	540
1	101	522
2	277	504
3	1080	492

Stop Event

1×	node limit

Counts

92 → 81

prune127.0ms (1.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	67	14	81
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	73	26	99

Error

22.8b

Counts

99 → 26

Alt Table

Status	Error	Program
	32.9b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	26.1b	(log1p.f64 (expm1.f64 (/.f64 1 (cos.f64 (*.f64 1/2 (/.f64 x y))))))
	25.9b	(/.f64 1 (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))) 3)))
	32.8b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 3))
	25.9b	(/.f64 1 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))))) 1))
	32.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2) 1) (/.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (sin.f64 (.f64 (/.f64 x y) 1/2))))
	26.3b	(/.f64 1 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))) 2)))
	61.5b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 x y) 1/2)))) (sin.f64 1))))
	25.9b	(/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))) 3))
	33.1b	(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	59.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	32.4b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))
	58.5b	(/.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (sin.f64 (/.f64 x (*.f64 y 2))))
	27.4b	(/.f64 1 (cos.f64 (cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3))))
	26.3b	(/.f64 1 (cos.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 3)))
	26.2b	1
▶	25.8b	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))
	35.0b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	54.1b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	28.0b	(/.f64 1 (cos.f64 (-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y)))) 1)))
	28.5b	(/.f64 1 (fma.f64 (/.f64 -1/8 y) (/.f64 x (/.f64 y x)) 1))
	59.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	43.9b	(/.f64 1 (cos.f64 (pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)))
	35.0b	(/.f64 1 (cos.f64 (pow.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)))
	45.5b	(/.f64 1 (cos.f64 (/.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 y)) (sqrt.f64 y))))
	30.0b	(/.f64 1 (cos.f64 (/.f64 (/.f64 (.f64 1/2 x) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))))

Compiler

Compiled 2065 to 1523 computations (26.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))
✓	0.3b	(/.f64 1/2 (/.f64 y x))
✓	25.8b	(cos.f64 (/.f64 1/2 (/.f64 y x)))

series28.0ms (0.4%)

Counts

3 → 72

Calls

18 calls:

4.0ms	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))	y	0
3.0ms	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))	x	-inf
3.0ms	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))	x	inf
2.0ms	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))	x	0
2.0ms	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))	y	-inf

rewrite47.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

872×	`log1p-expm1-u_binary64`
872×	`expm1-log1p-u_binary64`
223×	`prod-diff_binary64`
95×	`add-sqr-sqrt_binary64`
88×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	192	28
2	2426	28

Stop Event

1×	node limit

Counts

3 → 74

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

837×	`associate-/l*_binary64`
622×	`associate-/r*_binary64`
414×	`fma-def_binary64`
387×	`associate-*l/_binary64`
143×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	960
1	109	942
2	287	924
3	1107	912

Stop Event

1×	node limit

Counts

146 → 92

prune118.0ms (1.7%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	3	22	25
Picked	0	1	1
Done	0	0	0
Total	91	27	118

Error

22.8b

Counts

118 → 27

Alt Table

Status	Error	Program
	32.9b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	26.1b	(log1p.f64 (expm1.f64 (/.f64 1 (cos.f64 (*.f64 1/2 (/.f64 x y))))))
	32.8b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 3))
	25.9b	(/.f64 1 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))))) 1))
	32.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2) 1) (/.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (sin.f64 (.f64 (/.f64 x y) 1/2))))
	26.3b	(/.f64 1 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))) 2)))
	61.5b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 x y) 1/2)))) (sin.f64 1))))
▶	25.9b	(/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))) 3))
	33.1b	(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	59.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	32.4b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))
	27.4b	(/.f64 1 (cos.f64 (cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3))))
	26.8b	(/.f64 1 (cos.f64 (sqrt.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)))))
	35.0b	(/.f64 1 (cos.f64 (pow.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)))
	43.0b	(/.f64 1 (cos.f64 (.f64 (.f64 (/.f64 1/2 y) (sqrt.f64 x)) (sqrt.f64 x))))
	45.5b	(/.f64 1 (cos.f64 (/.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 y)) (sqrt.f64 y))))
	29.5b	(/.f64 1 (cos.f64 (.f64 (.f64 (/.f64 1/2 y) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))))
	30.0b	(/.f64 1 (cos.f64 (/.f64 (/.f64 (.f64 1/2 x) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))))
	25.9b	(/.f64 1 (cos.f64 (.f64 (cbrt.f64 (.f64 1/2 (/.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 2))))
✓	25.8b	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))
	35.0b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	54.1b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	28.0b	(/.f64 1 (cos.f64 (-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y)))) 1)))
	28.5b	(/.f64 1 (fma.f64 (/.f64 -1/8 y) (/.f64 x (/.f64 y x)) 1))
	59.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	43.9b	(/.f64 1 (cos.f64 (pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)))
	26.2b	1

Compiler

Compiled 2174 to 1596 computations (26.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))) 3))
✓	0.3b	(cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))))
✓	0.3b	(pow.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))) 3)
	25.9b	(cos.f64 (*.f64 1/2 (/.f64 x y)))

series178.0ms (2.5%)

Counts

3 → 72

Calls

18 calls:

27.0ms	(pow.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))) 3)	x	inf
24.0ms	(pow.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))) 3)	y	0
24.0ms	(pow.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))) 3)	x	-inf
21.0ms	(cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))))	x	-inf
21.0ms	(cbrt.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))))	x	inf

rewrite51.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

498×	`log-prod_binary64`
243×	`prod-diff_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
173×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	250	32
2	2814	32

Stop Event

1×	node limit

Counts

3 → 88

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

651×	`fma-def_binary64`
585×	`associate-*l/_binary64`
321×	`cancel-sign-sub-inv_binary64`
230×	`fma-neg_binary64`
187×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1188
1	157	1170
2	423	1146
3	1648	1128

Stop Event

1×	node limit

Counts

160 → 111

prune264.0ms (3.8%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	133	8	141
Fresh	4	21	25
Picked	1	0	1
Done	0	1	1
Total	138	30	168

Error

22.8b

Counts

168 → 30

Alt Table

Status	Error	Program
	28.3b	(/.f64 1 (pow.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 (.f64 1/2 x) y))))) (cbrt.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 (.f64 1/2 x) y))))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 (.f64 1/2 x) y))))))) 3))
	32.9b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	32.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2) 1) (/.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (sin.f64 (.f64 (/.f64 x y) 1/2))))
	26.3b	(/.f64 1 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))) 2)))
	27.5b	(/.f64 1 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (.f64 1/2 x) y)))) (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (.f64 1/2 x) y)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (.f64 1/2 x) y)))))))
	59.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	28.1b	(/.f64 1 (+.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 (/.f64 (.f64 1/2 x) y)))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 (/.f64 (.f64 1/2 x) y)))) (sin.f64 1))))
	33.1b	(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	28.5b	(/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 -1/8 y) (/.f64 x (/.f64 y x)) 1)) 3))
	59.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	25.9b	(/.f64 1 (pow.f64 (cbrt.f64 (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))))) 3))
	27.4b	(/.f64 1 (cos.f64 (cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3))))
	26.8b	(/.f64 1 (cos.f64 (sqrt.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)))))
	35.0b	(/.f64 1 (cos.f64 (pow.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)))
	43.0b	(/.f64 1 (cos.f64 (.f64 (.f64 (/.f64 1/2 y) (sqrt.f64 x)) (sqrt.f64 x))))
	45.5b	(/.f64 1 (cos.f64 (/.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 y)) (sqrt.f64 y))))
	29.5b	(/.f64 1 (cos.f64 (.f64 (.f64 (/.f64 1/2 y) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))))
	30.0b	(/.f64 1 (cos.f64 (/.f64 (/.f64 (.f64 1/2 x) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))))
	25.9b	(/.f64 1 (pow.f64 (log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (cos.f64 (/.f64 (*.f64 1/2 x) y)))))) 3))
	25.9b	(/.f64 1 (cos.f64 (.f64 (cbrt.f64 (.f64 1/2 (/.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 2))))
✓	25.8b	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))
	35.0b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	26.3b	(/.f64 1 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (*.f64 1/2 x) y))) 2)) 3))
	25.9b	(/.f64 1 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (*.f64 1/2 x) y)))) 3) 3))
	54.1b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	28.0b	(/.f64 1 (cos.f64 (-.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y)))) 1)))
	25.9b	(/.f64 1 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 1/2 (/.f64 x y))))) 1))
	61.5b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 x y) 1/2)))) (sin.f64 1))))
	43.9b	(/.f64 1 (cos.f64 (pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)))
	26.2b	1

Compiler

Compiled 2969 to 2332 computations (21.5% saved)

regimes667.0ms (9.6%)

Accuracy

Total 2.8b remaining (10%)

Threshold costs 0b (0%)

Counts

122 → 2

Compiler

Compiled 11629 to 8995 computations (22.7% saved)

bsearch0.0ms (0%)

Algorithm

1×	binary-search

Calls

1 calls:

0.0ms

(/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))

Steps

Iters	Point		Range
1.3008624647609368	∈ [	1.2716990814678844	,	1.3300258480539893	]

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	17	46

Stop Event

1×

saturated

end463.0ms (6.7%)

Stop Event

1×

fuel

Compiler

Compiled 669 to 521 computations (22.1% saved)

Details

analyze1.1s (16.1%)

sample3.4s (48.5%)

preprocess14.0ms (0.2%)

simplify11.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series60.0ms (0.9%)

rewrite53.0ms (0.8%)

simplify46.0ms (0.7%)

prune125.0ms (1.8%)

localize10.0ms (0.1%)

series29.0ms (0.4%)

rewrite49.0ms (0.7%)

simplify27.0ms (0.4%)

prune127.0ms (1.8%)

localize6.0ms (0.1%)

series28.0ms (0.4%)

rewrite47.0ms (0.7%)

simplify34.0ms (0.5%)

prune118.0ms (1.7%)

localize8.0ms (0.1%)

series178.0ms (2.5%)

rewrite51.0ms (0.7%)

simplify39.0ms (0.6%)

prune264.0ms (3.8%)

regimes667.0ms (9.6%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end463.0ms (6.7%)

Profiling